a staggeringly easy and cheap but surprisingly rich sauce is the marcella hazan one:
onion, peeled and halved
tin of good quality whole or chopped tomatoes
2tbl sp butter
simmer in a pan for about 30-45 mins until really thick, lid off, stir occasionally
save the onion for another meal, the sauce can be kept in an airtight container in the fridge for up to a week or in the freezer.
at this stage you have many options like using it as a pizza sauce or as a base for a chilli but for the dish you want to re-create yes either stir in a dollop of soft cheese or a glug of cream, fold into cooked pasta with some melty cheese and some parmesan and bake. This is great with gnocchi instead of the pasta and a cheesy breadcrumb topping.
I make this sauce every few weeks as so handy to have in the fridge and cheaper and nicer than a jar of 'pasta sauce'.
Another option which I had made many a mid-week is: tin of tomatoes, half a cup of cream, leftover bits and bobs of cheese, basil or dried herbs, cooked pasta like tubes or spirals, black pepper. bake at 400 for 30 mins, foil on if it gets a bit too brown but I do like crunchy pasta bits and almost burnt cheese